康德与黑格尔的数学观及其比较

发布时间：2018-01-06 11:40

本文关键词：康德与黑格尔的数学观及其比较　出处：《四川师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：在西方文明中,数学一直占有极其重要的地位,它不仅在自然科学、雕塑、音乐、建筑等方面有着决定性作用,同时也影响了一批哲学家的思想与研究方法。数学是人类运用理性能力最辉煌的体现,数学成为真理的化身。因为数学的量化研究,数学知识被认为是最具确定性的。这种关于数学确定性的观点起源于毕达哥拉斯学派,在近代思想中达到了顶峰。像开普勒、哥白尼、笛卡尔、牛顿等人都对数学的确定性毫不怀疑,哲学家斯宾诺莎甚至用几何学的论证方式来考察实体(自然、上帝)、心灵和情感。在学界普遍推崇数学的背景下,哲学家们也大都认为数学是哲学的理想,哲学应当效仿数学。但是,康德与黑格尔却对数学进行了深刻的反思。康德对数学的确定性是非常认同的。他认为数学命题是先天综合判断,是建立在纯直观之上的知识,不依赖于后天经验,具有最高等级的确定性。数学是理性运用的光辉范例,是哲学应该效仿的对象。所以,他想仿照数学与自然科学来构建其形而上学。同时,在康德这里,数学与哲学也是相互论证的,数学是哲学的样板,而哲学为数学奠基。但是,康德又指出,数学与哲学是两种不同种类的知识,二者有着本质的区别,它们是理性能力的双重运用,数学中的定义、公理与演证方法并不适用于哲学。如果只是仿照数学的方法来构建哲学,将对哲学造成极大的伤害。而黑格尔对数学进行了更为彻底的批判。他认为,数学关心的是数量关系,不是本质的运动;“数”只是最接近感性事物的思想;数学知识是无概念的运动;数学证明的运动只是一种外在于对象的行为;数学的自明性是建立在目的贫乏和材料的空虚上的。因而,数学命题只是空洞的、僵死的形式。数学中并没有真正哲学意义上的真理。如果用数学知识来解释绝对精神,只是将其塑造成一个毫无生命力的机器。所以,数学根本不可能是哲学最后的理想。可以看出,纵使黑格尔与康德对数学有着截然不同的态度,但两人都认为数学与哲学有着本质的区别,也都认为运用数学方法来构建哲学是不可取的。本文梳理了康德与黑格尔的数学观点,并从数学真理性、时空观和数学与哲学的关系三个方面将二者进行了比较。两人的数学观不同,反映的是两人的哲学观不同:康德关注现象的知识,现象处于时空中,都是可以量化处理的,所以数学很重要,这是康德重视数学的哲学基础。但是,黑格尔认为,数学只能处理有形的物理现象,只是知性层面的片面知识。黑格尔关注的并不是现象世界更不是有广延的事物,而是绝对精神及其演变,绝对精神不能被量化处理,所以数学在黑格尔那里显然不重要。
[Abstract]:Mathematics has always played a very important role in western civilization. It not only plays a decisive role in natural science, sculpture, music, architecture and so on. At the same time, it also influenced the thought and research method of a group of philosophers. Mathematics is the most brilliant embodiment of human's ability to use reason, mathematics becomes the embodiment of truth, because of the quantitative study of mathematics. Mathematical knowledge is considered to be the most deterministic. This view of mathematical certainty originated from the Pythagorean school and reached its peak in modern thought, such as Kepler, Copernicus, Descartes. Newton and others had no doubt about the certainty of mathematics, and the philosopher Spinoza even examined substance (nature, God, mind and emotion) in a geometric way. Philosophers also think that mathematics is the ideal of philosophy, philosophy should imitate mathematics, but. Kant and Hegel, however, deeply reflect on mathematics. Kant agrees very much with the certainty of mathematics. He thinks that mathematical proposition is innate comprehensive judgment and is based on pure intuitive knowledge. Mathematics is the shining example of rational application and the object that philosophy should emulate. Therefore, he wants to imitate mathematics and natural science to construct its metaphysics. At the same time. In Kant's case, mathematics and philosophy also demonstrate each other, mathematics is the model of philosophy, and philosophy lays the foundation for mathematics. However, Kant points out that mathematics and philosophy are two different kinds of knowledge. There is an essential difference between them. They are the dual application of rational ability, the definition in mathematics, axiom and proof method are not applicable to philosophy, if only imitate the method of mathematics to construct philosophy. It will do great harm to philosophy. Hegel criticizes mathematics more thoroughly. He thinks that mathematics is concerned with quantity relation, not essential movement; "number" is only the thought closest to the perceptual thing; Mathematical knowledge is a motion without concept; The motion of mathematical proof is only a kind of behavior which lies outside the object; The self-evident nature of mathematics is based on the scarcity of purpose and the emptiness of materials. Therefore, the mathematical proposition is only empty. Dead form. There is no true philosophical truth in mathematics. If the absolute spirit is explained by mathematical knowledge, it is only shaped into a lifeless machine. Mathematics can not be the last ideal of philosophy. It can be seen that even though Hegel and Kant have different attitudes to mathematics, they both think that mathematics and philosophy have essential differences. It is also considered that it is not advisable to use mathematical method to construct philosophy. This paper combs Kant's and Hegel's viewpoint of mathematics, and analyzes the truth of mathematics. The view of time and space and the relationship between mathematics and philosophy are compared. The difference between them reflects the difference between them: Kant pays attention to the knowledge of phenomenon and the phenomenon is in time and space. Mathematics is very important, which is the philosophical basis of Kant's emphasis on mathematics. However, Hegel believes that mathematics can only deal with tangible physical phenomena. What Hegel focuses on is not the phenomenon world nor the extensive things, but the absolute spirit and its evolution, and absolute spirit can not be quantified. So mathematics is obviously not important in Hegel's.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：B516.3

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